Let G $=($V$,$ E$)$ be a directed graph with nonnegative edge costs c : E $->$ N$.$

We seek a subset S $$ V that maximizes the total cost of edges going out of S;

Give a greedy algorithm for the above problem

with an approximation guarantee of $1/4.$

please give me a detailed algorithm and very detailed approximation proof because the once given on this website are not enough detailed for me to understand how we proved the approximation

thank you